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Cholesky decomposition class
For a symmetric, positive definite matrix A, the Cholesky decomposition
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For an m-by-n matrix A with m &gt;= n, the LU decomposition is an m-by-n
unit lower triangular matrix L, an n-by-n upper triangular matrix U,
and a permutation vector piv of length m so that A(piv,:) = L*U</a></li>
<li><a href="../packages/JAMA%0D%0AFor%20an%20m-by-n%20matrix%20A%20with%20m%20&gt;=%20n,%20the%20QR%20decomposition%20is%20an%20m-by-n%0D%0Aorthogonal%20matrix%20Q%20and%20an%20n-by-n%20upper%20triangular%20matrix%20R%20so%20that%0D%0AA%20=%20Q*R.html"><i class="icon-folder-open"></i> JAMA
For an m-by-n matrix A with m &gt;= n, the QR decomposition is an m-by-n
orthogonal matrix Q and an n-by-n upper triangular matrix R so that
A = Q*R</a></li>
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For an m-by-n matrix A with m &gt;= n, the singular value decomposition is
an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
an n-by-n orthogonal matrix V so that A = U*S*V'</a></li>
<li><a href="../packages/JAMA%0D%0APythagorean%20Theorem:%0D%0Aa%20=%203%0D%0Ab%20=%204%0D%0Ar%20=%20sqrt(square(a)%20+%20square(b))%0D%0Ar%20=%205%0D%0Ar%20=%20sqrt(a%5E2%20+%20b%5E2)%20without%20under.overflow.html"><i class="icon-folder-open"></i> JAMA
Pythagorean Theorem:
a = 3
b = 4
r = sqrt(square(a) + square(b))
r = 5
r = sqrt(a^2 + b^2) without under/overflow</a></li>
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<li class="nav-header">
<i class="icon-custom icon-method"></i> Methods
                    <ul>
<li class="method public inherited"><a href="#method__DataLen" title="_DataLen :: Returns the amount of data saved for this PPS"><span class="description">Returns the amount of data saved for this PPS</span><pre>_DataLen()</pre></a></li>
<li class="method public "><a href="#method___construct" title="__construct :: The constructor"><span class="description">The constructor</span><pre>__construct()</pre></a></li>
<li class="method public inherited"><a href="#method__getPpsWk" title="_getPpsWk :: Returns a string with the PPS's WK (What is a WK?)"><span class="description">Returns a string with the PPS's WK (What is a WK?)</span><pre>_getPpsWk()</pre></a></li>
<li class="method public inherited"><a href="#method__savePpsSetPnt" title="_savePpsSetPnt :: Updates index and pointers to previous, next and children PPS's for this
PPS."><span class="description">Updates index and pointers to previous, next and children PPS's for this
PPS.</span><pre>_savePpsSetPnt()</pre></a></li>
<li class="method public "><a href="#method_append" title="append :: Append data to PPS"><span class="description">Append data to PPS</span><pre>append()</pre></a></li>
<li class="method public "><a href="#method_getStream" title="getStream :: Returns a stream for reading this file using fread() etc."><span class="description">Returns a stream for reading this file using fread() etc.</span><pre>getStream()</pre></a></li>
<li class="method public "><a href="#method_init" title="init :: Initialization method."><span class="description">Initialization method.</span><pre>init()</pre></a></li>
</ul>
</li>
<li class="nav-header">
<i class="icon-custom icon-property"></i> Properties
                    <ul>
<li class="property public inherited"><a href="#property_DirPps" title="$DirPps :: The index of it's first child if this is a Dir or Root PPS"><span class="description"></span><pre>$DirPps</pre></a></li>
<li class="property public inherited"><a href="#property_Name" title="$Name :: The PPS name (in Unicode)"><span class="description"></span><pre>$Name</pre></a></li>
<li class="property public inherited"><a href="#property_NextPps" title="$NextPps :: The index of the next PPS"><span class="description"></span><pre>$NextPps</pre></a></li>
<li class="property public inherited"><a href="#property_No" title="$No :: The PPS index"><span class="description"></span><pre>$No</pre></a></li>
<li class="property public inherited"><a href="#property_PrevPps" title="$PrevPps :: The index of the previous PPS"><span class="description"></span><pre>$PrevPps</pre></a></li>
<li class="property public inherited"><a href="#property_Size" title="$Size :: The size of the PPS's data (in bytes)"><span class="description"></span><pre>$Size</pre></a></li>
<li class="property public inherited"><a href="#property_Time1st" title="$Time1st :: A timestamp"><span class="description"></span><pre>$Time1st</pre></a></li>
<li class="property public inherited"><a href="#property_Time2nd" title="$Time2nd :: A timestamp"><span class="description"></span><pre>$Time2nd</pre></a></li>
<li class="property public inherited"><a href="#property_Type" title="$Type :: The PPS type."><span class="description"></span><pre>$Type</pre></a></li>
<li class="property public inherited"><a href="#property__StartBlock" title="$_StartBlock :: Starting block (small or big) for this PPS's data  inside the container"><span class="description"></span><pre>$_StartBlock</pre></a></li>
<li class="property public inherited"><a href="#property__data" title="$_data :: The PPS's data (only used if it's not using a temporary file)"><span class="description"></span><pre>$_data</pre></a></li>
<li class="property public inherited"><a href="#property_children" title="$children :: Array of child PPS's (only used by Root and Dir PPS's)"><span class="description"></span><pre>$children</pre></a></li>
<li class="property public inherited"><a href="#property_ole" title="$ole :: Pointer to OLE container"><span class="description"></span><pre>$ole</pre></a></li>
</ul>
</li>
</ul>
</div>
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<span class="divider">\</span><a href="../classes/PHPExcel_Shared_OLE_PPS_File.html">PHPExcel_Shared_OLE_PPS_File</a>
</li>
</ul>
<div class="element class">
<p class="short_description">Class for creating File PPS's for OLE containers</p>
<div class="details">
<div class="long_description"></div>
<table class="table table-bordered">
<tr>
<th>author</th>
<td><a href="mailto:xnoguer@php.net">Xavier Noguer</a></td>
</tr>
<tr>
<th>category</th>
<td>PHPExcel</td>
</tr>
<tr>
<th>package</th>
<td><a href="../packages/PHPExcel.Shared.OLE.html">PHPExcel_Shared_OLE</a></td>
</tr>
</table>
<h3>
<i class="icon-custom icon-method"></i> Methods</h3>
<a id="method__DataLen"></a><div class="element clickable method public method__DataLen" data-toggle="collapse" data-target=".method__DataLen .collapse">
<h2>Returns the amount of data saved for this PPS</h2>
<pre>_DataLen() : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered">
<tr>
<th>access</th>
<td>public</td>
</tr>
<tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::_DataLen()</td>
</tr>
</table>
<h3>Returns</h3>
<div class="subelement response">
<code>integer</code>The amount of data (in bytes)</div>
</div></div>
</div>
<a id="method___construct"></a><div class="element clickable method public method___construct" data-toggle="collapse" data-target=".method___construct .collapse">
<h2>The constructor</h2>
<pre>__construct(string $name) </pre>
<div class="labels"></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered">
<tr>
<th>access</th>
<td>public</td>
</tr>
<tr>
<th>see</th>
<td><a href="">\OLE::Asc2Ucs()</a></td>
</tr>
</table>
<h3>Parameters</h3>
<div class="subelement argument">
<h4>$name</h4>
<code>string</code><p>The name of the file (in Unicode)</p>
</div>
</div></div>
</div>
<a id="method__getPpsWk"></a><div class="element clickable method public method__getPpsWk" data-toggle="collapse" data-target=".method__getPpsWk .collapse">
<h2>Returns a string with the PPS's WK (What is a WK?)</h2>
<pre>_getPpsWk() : string</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered">
<tr>
<th>access</th>
<td>public</td>
</tr>
<tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::_getPpsWk()</td>
</tr>
</table>
<h3>Returns</h3>
<div class="subelement response">
<code>string</code>The binary string</div>
</div></div>
</div>
<a id="method__savePpsSetPnt"></a><div class="element clickable method public method__savePpsSetPnt" data-toggle="collapse" data-target=".method__savePpsSetPnt .collapse">
<h2>Updates index and pointers to previous, next and children PPS's for this
PPS.</h2>
<pre>_savePpsSetPnt(array $raList, $to_save, $depth) : integer</pre>
<div class="labels">
<span class="label">Inherited</span><span class="label">Static</span>
</div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"><p>I don't think it'll work with Dir PPS's.</p></div>
<table class="table table-bordered">
<tr>
<th>access</th>
<td>public</td>
</tr>
<tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::_savePpsSetPnt()</td>
</tr>
</table>
<h3>Parameters</h3>
<div class="subelement argument">
<h4>$raList</h4>
<code>array</code><p>&$raList Reference to the array of PPS's for the whole OLE
                         container</p>
</div>
<div class="subelement argument"><h4>$to_save</h4></div>
<div class="subelement argument"><h4>$depth</h4></div>
<h3>Returns</h3>
<div class="subelement response">
<code>integer</code>The index for this PPS</div>
</div></div>
</div>
<a id="method_append"></a><div class="element clickable method public method_append" data-toggle="collapse" data-target=".method_append .collapse">
<h2>Append data to PPS</h2>
<pre>append(string $data) </pre>
<div class="labels"></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>access</th>
<td>public</td>
</tr></table>
<h3>Parameters</h3>
<div class="subelement argument">
<h4>$data</h4>
<code>string</code><p>The data to append</p></div>
</div></div>
</div>
<a id="method_getStream"></a><div class="element clickable method public method_getStream" data-toggle="collapse" data-target=".method_getStream .collapse">
<h2>Returns a stream for reading this file using fread() etc.</h2>
<pre>getStream() : resource</pre>
<div class="labels"></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<h3>Returns</h3>
<div class="subelement response">
<code>resource</code>a read-only stream</div>
</div></div>
</div>
<a id="method_init"></a><div class="element clickable method public method_init" data-toggle="collapse" data-target=".method_init .collapse">
<h2>Initialization method.</h2>
<pre>init() : mixed</pre>
<div class="labels"></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"><p>Has to be called right after OLE_PPS_File().</p></div>
<table class="table table-bordered"><tr>
<th>access</th>
<td>public</td>
</tr></table>
<h3>Returns</h3>
<div class="subelement response">
<code>mixed</code>true on success</div>
</div></div>
</div>
<h3>
<i class="icon-custom icon-property"></i> Properties</h3>
<a id="property_DirPps"> </a><div class="element clickable property public property_DirPps" data-toggle="collapse" data-target=".property_DirPps .collapse">
<h2></h2>
<pre>$DirPps : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$DirPps</td>
</tr></table>
</div></div>
</div>
<a id="property_Name"> </a><div class="element clickable property public property_Name" data-toggle="collapse" data-target=".property_Name .collapse">
<h2></h2>
<pre>$Name : string</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$Name</td>
</tr></table>
</div></div>
</div>
<a id="property_NextPps"> </a><div class="element clickable property public property_NextPps" data-toggle="collapse" data-target=".property_NextPps .collapse">
<h2></h2>
<pre>$NextPps : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$NextPps</td>
</tr></table>
</div></div>
</div>
<a id="property_No"> </a><div class="element clickable property public property_No" data-toggle="collapse" data-target=".property_No .collapse">
<h2></h2>
<pre>$No : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$No</td>
</tr></table>
</div></div>
</div>
<a id="property_PrevPps"> </a><div class="element clickable property public property_PrevPps" data-toggle="collapse" data-target=".property_PrevPps .collapse">
<h2></h2>
<pre>$PrevPps : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$PrevPps</td>
</tr></table>
</div></div>
</div>
<a id="property_Size"> </a><div class="element clickable property public property_Size" data-toggle="collapse" data-target=".property_Size .collapse">
<h2></h2>
<pre>$Size : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$Size</td>
</tr></table>
</div></div>
</div>
<a id="property_Time1st"> </a><div class="element clickable property public property_Time1st" data-toggle="collapse" data-target=".property_Time1st .collapse">
<h2></h2>
<pre>$Time1st : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$Time1st</td>
</tr></table>
</div></div>
</div>
<a id="property_Time2nd"> </a><div class="element clickable property public property_Time2nd" data-toggle="collapse" data-target=".property_Time2nd .collapse">
<h2></h2>
<pre>$Time2nd : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$Time2nd</td>
</tr></table>
</div></div>
</div>
<a id="property_Type"> </a><div class="element clickable property public property_Type" data-toggle="collapse" data-target=".property_Type .collapse">
<h2></h2>
<pre>$Type : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"><p>Dir, Root or File</p></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$Type</td>
</tr></table>
</div></div>
</div>
<a id="property__StartBlock"> </a><div class="element clickable property public property__StartBlock" data-toggle="collapse" data-target=".property__StartBlock .collapse">
<h2></h2>
<pre>$_StartBlock : integer</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$_StartBlock</td>
</tr></table>
</div></div>
</div>
<a id="property__data"> </a><div class="element clickable property public property__data" data-toggle="collapse" data-target=".property__data .collapse">
<h2></h2>
<pre>$_data : string</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$_data</td>
</tr></table>
</div></div>
</div>
<a id="property_children"> </a><div class="element clickable property public property_children" data-toggle="collapse" data-target=".property_children .collapse">
<h2></h2>
<pre>$children : array</pre>
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<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$children</td>
</tr></table>
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</div>
<a id="property_ole"> </a><div class="element clickable property public property_ole" data-toggle="collapse" data-target=".property_ole .collapse">
<h2></h2>
<pre>$ole : \OLE</pre>
<div class="labels"><span class="label">Inherited</span></div>
<div class="row collapse"><div class="detail-description">
<div class="long_description"></div>
<table class="table table-bordered"><tr>
<th>inherited_from</th>
<td>\PHPExcel_Shared_OLE_PPS::$$ole</td>
</tr></table>
</div></div>
</div>
</div>
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